There is another factor at work here, a very common problem yet rarely perceived.
Havoc, by any chance do you use any level of gunzoom while shooting at the target? Because, fine tuning plane movement during zoomed-in status will exaggerate the effects of stick movement.
I for one, need glasses and don't have good eyesight. I use a 17" monitor and still can't really make out a silhouette of a plane when the distance marker is further than 400. Only inside 400yards, I can really see the whole of the target plane to aim at normal head/non-zoomed position. For many other reasons than just eyesight, a lot of people use zoomed in views to confirm the position of the enemy plane. Many of these people also prefer to shoot at the enemy plane while the view is zoomed in.
However, they will soon realize that shooting at the general position of an enemy plane with an unclear view in the unzoomed position(where you can't really make out the silhouette fully), will more often than not offer better results than being zoomed in (and having a clr view of the plane).
This is because, the ratio of nose movement between the zoomed in and unzoomed in views is different even with the same amount of pitch control.
For instance, if a very slight stick input will change the aiming point by about 1cm in an unzoomed view, if you are zoomed in by double the same stick movement will change the aim by 2cm. So what typically happens, is that people zoom in, aim at the target, and then think to themselves "let's change the aim by 1cm and then I will have him"... except as you most slightly pull the stick the nose pitch will change by 2cm and your aim thrown off 1cm due to overcontrol.
The distance is closing, you are getting anxious, you try to correct the aim.. and the more you try to correct it, the more the aim is thrown off and the nose seems to "bounce around".
It's the exact same thing with rudder control(which is very important in aiming, too). Aileron control is uneffected by zoom, since there is no distortion in relative distances in the roll axis whether or not the view is zoomed in.
To be able to fine control your pitch/yaw axis while zoomed in, you have to meddle with the stick settings so that the sliders correspond to very very small amount of pitch movement - except, if you do this, it may be easier to aim, but controlling your plane during normal flight becomes much more harder.
Thus, the best way to avoid the "nose-bounce" in this case is;
1) if you have good eyesight, get used to shooting from unzoomed position
2) if you have bad eyesight, get in really close to the target(under 400, preferably when the distance marker shows '200')
3) or, practice positional estimation and defelction shooting, so you can pick a point where the enemy plane will pass, zoom in, and then shoot there... so you don't have to 'tracking' the target with the gunsight at all(which, by tracking him, will force you to fine tune aiming more and more)
In my case, I've given up shooting over 400yd marker, so I get within the distance where I can see the enemy plane clearly without having to use zoom. I use zoom only when I am shooting at stationary targets, like enemy planes escaping by level flight(I'll zoom in fully in this case, and if my plane has nose mounted machine guns, will try to hurt him upto until 600~800. If my plane has wingarmament, I just give up), or when strafing GV with IL2 or Hurri2D, or when attacking ground targets.